Several complications would remain to be addressed.
Software for Alternate Link Functions. If it is discovered that an alternate link function is preferred, it might require a modest amount of software development to implement. However, this should be relatively straightforward in either SAS or R, which are two standard statistical software systems that the Census Bureau uses.
Loss Function or Objective Functions for Assessing Fit of Models. Another complication is that the current loss function underlying the fitting of the coefficients of these logistic regression models is implicit in the separate likelihood equations for the two models and is therefore somewhat disconnected from the ultimate goal, which is to predict the population size or, what amounts to the same thing, net coverage error. It may be that the ultimate goal can be better represented by weighting the likelihood equations to take this modified objective function into account. The Census Bureau has done some work in this direction and we support this research and its implementation if it is found to provide preferred estimates.
Measurement Error. Census data are subject to measurement error, and these errors will have deleterious effects on the application of logistic regression models. If the measurement error is unrelated to the outcome (match status or correct enumeration status), the effect on the data is the attenuation of relationships. In other words, the predictors will not be as effective without the measurement error. But if the measurement error is related to the outcomes, the effect could be much more complicated, including the introduction of severe biases.